Finite Group Databasebeta

← #26139947

Subgroups — #26139947

Order 12032.

1862 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15688996C211yesmaximal, characteristic
2C2×C4×C22⋊Dic47C211yesmaximal, characteristic
3#20241654C212yesmaximal, complemented
4#20241648C212yesmaximal, complemented
5#20241619C212yesmaximal, complemented
6#20241612C212yesmaximal, complemented
7#20241611C211yesmaximal, characteristic
8#20241611C211yesmaximal, characteristic
9#20241611C211yesmaximal, characteristic
10#20241611C211yesmaximal, characteristic
11C22×#95×C47C211yesmaximal, characteristic
12C22×Dic47⋊C4C2212yes—
13C22×C22⋊Dic47C2211yescharacteristic
14C22×C22⋊Dic47C2211yescharacteristic
15C22×C22⋊Dic47C2211yescharacteristic
16C22×C22⋊Dic47C2211yescharacteristic
17C22×C4×Dic47C2211yescharacteristic
18C22×C4×Dic47C2211yescharacteristic
19#15688996C418yescomplemented
20C4×C22⋊Dic47—24no—
21C2×C47⋊#95C2212yes—
22C2×C47⋊#95C2212yes—
23C2×C47⋊#95C2212yes—
24C2×C47⋊#95C2211yescharacteristic
25C2×C47⋊#95C2211yescharacteristic
26C2×C47⋊#95C2212yes—
27C2×C47⋊#95C2212yes—
28C2×C47⋊#95C2212yes—
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2212yes—
32C24×C4×C47C2211yescharacteristic
33C24×C4×C47C2211yescharacteristic
34C24×C4×C47C2211yescharacteristic
35C2×#95×C47—24no—
36C2×#95×C47C2212yes—
37C2×#95×C47C2212yes—
38C23×Dic47C2312yes—
39C23×Dic47C2311yescharacteristic
40C23×Dic47C2312yes—
41C23×Dic47C2311yescharacteristic
42C23×Dic47C2311yescharacteristic
43C23×Dic47C2311yescharacteristic
44C2×Dic47⋊C4—42no—
45C2×Dic47⋊C4—42no—
46C2×Dic47⋊C4C2×C418yescomplemented
47C2×C22⋊Dic47—22no—
48C2×C22⋊Dic47—22no—
49C2×C22⋊Dic47—22no—
50C2×C22⋊Dic47—22no—
51C2×C22⋊Dic47—22no—
52C2×C22⋊Dic47—22no—
53C2×C22⋊Dic47—22no—
54C2×C22⋊Dic47—22no—
55C2×C22⋊Dic47—22no—
56C2×C22⋊Dic47C2×C414yes—
57C2×C22⋊Dic47C2×C414yes—
58C2×C22⋊Dic47Q814yes—
59C2×C4×Dic47—22no—
60C2×C4×Dic47—22no—
61C2×C4×Dic47—24no—
62C2×C4×Dic47—42no—
63C47⋊#95—22no—
64C47⋊#95—22no—
65C47⋊#95—24no—
66C47⋊#95—24no—
67C47⋊#95—24no—
68C47⋊#95—42no—
69C47⋊#95—42no—
70C47⋊#95—42no—
71C47⋊#95—42no—
72C47⋊#95—42no—
73C47⋊#95C2×C418yescomplemented
74C25×C47C2311yescharacteristic
75C23×C4×C47—22no—
76C23×C4×C47—22no—
77C23×C4×C47—22no—
78C23×C4×C47—22no—
79C23×C4×C47—22no—
80C23×C4×C47—24no—
81C23×C4×C47—24no—
82C23×C4×C47—22no—
83C23×C4×C47—22no—
84C23×C4×C47—42no—
85C23×C4×C47—42no—
86C23×C4×C47—42no—
87C23×C4×C47—42no—
88C23×C4×C47C2×C414yes—
89C23×C4×C47D414yes—
90C23×C4×C47C2312yes—
91C23×C4×C47C2311yescharacteristic
92C23×C4×C47C2312yes—
93C23×C4×C47C2311yescharacteristic
94#95×C47—24no—
95#95×C47—24no—
96C24×C47—22no—
97C24×C47—22no—
98C24×C47—22no—
99C24×C47—22no—
100C24×C47C22×C412yes—
101C24×C47C2×D412yes—
102C24×C47C2×Q812yes—
103C24×C47#4112yes—
104C24×C47#4112yes—
105C24×C47#4112yes—
106C24×C47#4112yes—
107C24×C47C2411yescharacteristic
108C22×C4×C47—21no—
109C22×C4×C47—21no—
110C22×C4×C47—22no—
111C22×C4×C47—28no—
112C22×C4×C47—28no—
113C22×C4×C47—28no—
114C22×C4×C47—22no—
115C22×C4×C47—22no—
116C22×C4×C47—22no—
117C22×C4×C47—21no—
118C22×C4×C47—21no—
119C22×C4×C47—22no—
120C22×C4×C47—22no—
121C22×C4×C47—22no—
122C22×C4×C47—22no—
123C22×C4×C47—22no—
124C22×C4×C47—22no—
125C22×C4×C47—22no—
126C22×C4×C47—22no—
127C22×C4×C47—22no—
128C22×C4×C47—22no—
129C22×C4×C47—22no—
130C22×C4×C47—28no—
131C22×C4×C47—48no—
132C22×C4×C47—44no—
133C22×C4×C47—48no—
134C22×C4×C47—48no—
135C22×C4×C47—48no—
136C22×C4×C47—48no—
137C22×C4×C47—44no—
138C22×C4×C47—44no—
139C22×C4×C47—44no—
140C22×C4×C47—48no—
141C22×C4×C47—44no—
142C22×C4×C47C22×C414yes—
143C22×C4×C47C2×D412yes—
144C22×C4×C47C2×D412yes—
145C22×C4×C47#4114yes—
146C22×C4×C47#4114yes—
147C22×Dic47—21no—
148C22×Dic47—21no—
149C22×Dic47—21no—
150C22×Dic47—21no—
151C22×Dic47—22no—
152C22×Dic47—22no—
153C22×Dic47—22no—
154C22×Dic47—22no—
155C22×Dic47—22no—
156C22×Dic47—22no—
157C22×Dic47—22no—
158C22×Dic47—22no—
159C22×Dic47—21no—
160C22×Dic47—21no—
161C22×Dic47—21no—
162C22×Dic47—21no—
163C22×Dic47—22no—
164C22×Dic47—22no—
165C22×Dic47—22no—
166C22×Dic47—22no—
167C22×Dic47—22no—
168C22×Dic47—22no—
169C22×Dic47—22no—
170C22×Dic47—22no—
171C22×Dic47—22no—
172C22×Dic47—22no—
173C22×Dic47—22no—
174C22×Dic47—22no—
175C22×Dic47—22no—
176C22×Dic47C22×C412yes—
177C22×Dic47C22×C414yes—
178C22×Dic47C22×C412yes—
179C22×Dic47C2×Q812yes—
180C22×Dic47C2×Q812yes—
181C22⋊Dic47—28no—
182C22⋊Dic47—28no—
183C22⋊Dic47—28no—
184C22⋊Dic47—44no—
185Dic47⋊C4—48no—
186C4×Dic47—44no—
187C4×Dic47—44no—
188C23×C47—24no—
189C23×C47—24no—
190C23×C47—22no—
191C23×C47—22no—
192C23×C47—24no—
193C23×C47—22no—
194C23×C47—22no—
195C23×C47—24no—
196C23×C47—24no—
197C23×C47—24no—
198C23×C47—24no—
199C23×C47—24no—
200C23×C47—24no—
201C23×C47—24no—
202C23×C47—24no—
203C23×C47—24no—
204C23×C47#11714yes—
205C23×C47C4×D414yes—
206C23×C47C4×Q814yes—
207C23×C47C22⋊Q814yes—
208C23×C47#12314yes—
209C23×C47#12514yes—
210C23×C47#12614yes—
211C23×C47C23×C411yescharacteristic
212C23×C47C22×D411yescharacteristic
213C23×C47C22×Q811yescharacteristic
214C23×C47C2×#4111yescharacteristic
215C23×C47C2×#4111yescharacteristic
216C23×C47C2×#4111yescharacteristic
217C23×C47C2×#4112yes—
218C23×C47C2×#4112yes—
219C23×C47C2×#4111yescharacteristic
220C23×C47H(5,𝔽2)12yes—
221C23×C47H(5,𝔽2)12yes—
222C2×C4×C47—22no—
223C2×C4×C47—22no—
224C2×C4×C47—24no—
225C2×C4×C47—24no—
226C2×C4×C47—24no—
227C2×C4×C47—24no—
228C2×C4×C47—24no—
229C2×C4×C47—22no—
230C2×C4×C47—22no—
231C2×C4×C47—24no—
232C2×C4×C47—22no—
233C2×C4×C47—24no—
234C2×C4×C47—24no—
235C2×C4×C47—416no—
236C2×C4×C47—416no—
237C2×C4×C47—416no—
238C2×C4×C47—42no—
239C2×C4×C47—42no—
240C2×C4×C47—42no—
241C2×C4×C47—42no—
242C2×C4×C47—42no—
243C2×C4×C47—42no—
244C2×C4×C47—42no—
245C2×C4×C47—42no—
246C2×C4×C47—42no—
247C2×C4×C47—42no—
248C2×C4×C47#12314yes—
249C2×Dic47—24no—
250C2×Dic47—22no—
251C2×Dic47—22no—
252C2×Dic47—24no—
253C2×Dic47—24no—
254C2×Dic47—24no—
255C2×Dic47—24no—
256C2×Dic47—22no—
257C2×Dic47—22no—
258C2×Dic47—24no—
259C2×Dic47—24no—
260C2×Dic47—41no—
261C2×Dic47—41no—
262C2×Dic47—41no—
263C2×Dic47—41no—
264C2×Dic47—42no—
265C2×Dic47—41no—
266C2×Dic47—41no—
267C2×Dic47—41no—
268C2×Dic47—41no—
269C2×Dic47—42no—
270C2×Dic47—42no—
271C2×Dic47—42no—
272C2×Dic47—42no—
273C2×Dic47—42no—
274C2×Dic47—42no—
275C2×Dic47—42no—
276C2×Dic47—42no—
277C2×Dic47—42no—
278C2×Dic47—42no—
279C2×Dic47—42no—
280C2×Dic47—42no—
281C2×Dic47—42no—
282C2×Dic47—42no—
283#14040—471nomaximal, Sylow
284C22×C47—24no—
285C22×C47—24no—
286C22×C47—28no—
287C22×C47—28no—
288C22×C47—24no—
289C22×C47—24no—
290C22×C47—24no—
291C22×C47—28no—
292C22×C47—28no—
293C22×C47—24no—
294C22×C47#38718yes—
295C22×C47C2×#11711yescharacteristic
296C22×C47C2×C4×D411yescharacteristic
297C22×C47C2×C4×Q811yescharacteristic
298C22×C47C4×#4112yes—
299C22×C47#51812yes—
300C22×C47C2×C22⋊Q811yescharacteristic
301C22×C47C2×#12311yescharacteristic
302C22×C47C2×#12311yescharacteristic
303C22×C47#52511yescharacteristic
304C22×C47C2×#12511yescharacteristic
305C22×C47C2×#12611yescharacteristic
306C22×C47#52912yes—
307C22×C47#53411yescharacteristic
308C22×C47#53511yescharacteristic
309C22×C47#53812yes—
310C22×C47#55112yes—
311C22×C47#55112yes—
312C22×C47#55112yes—
313C22×C47#55112yes—
314C22×C47#55312yes—
315C22×C47#55312yes—
316C22×C47#55412yes—
317C22×C47#55412yes—
318C4×C47—24no—
319C4×C47—44no—
320C4×C47—44no—
321C4×C47—42no—
322Dic47—42no—
323Dic47—42no—
324Dic47—44no—
325Dic47—42no—
326Dic47—42no—
327Dic47—82no—
328C2×#385—471no—
329C2×C4×C22⋊C4—471no—
330C22×#95D4711yescharacteristic
331#1445—472no—
332#1443—472no—
333#1436—472no—
334#1434—472no—
335C22⋊#95—471no—
336C22⋊#95—471no—
337C22⋊#95—471no—
338C22⋊#95—471no—
339C2×C47—28no—
340C2×C47C2×#38711yescharacteristic
341C2×C47C4×#12311yescharacteristic
342C2×C47#232111yescharacteristic
343C2×C47#235312yes—
344C2×C47#236812yes—
345C2×C47#248211yescharacteristic
346C2×C47#248311yescharacteristic
347C2×C47#248711yescharacteristic
348C2×C47#250512yes—
349C2×C47#251012yes—
350C2×C47#257911yescharacteristic
351C24×C4C2×D4711yescharacteristic
352C24×C4C2×D4711yescharacteristic
353C24×C4C2×D4711yescharacteristic
354C22×C4⋊C4—472no—
355C22×C22⋊C4—471no—
356C22×C22⋊C4—471no—
357C22×C22⋊C4—471no—
358C22×C22⋊C4—471no—
359C22×C42—471no—
360C22×C42—471no—
361#385—478no—
362C4×C22⋊C4—944no—
363C2×#95—24no—
364C2×#95—472no—
365C2×#95—472no—
366C2×#95—472no—
367C2×#95—472no—
368C2×#95—471no—
369C2×#95—471no—
370C2×#95—472no—
371C2×#95—472no—
372C2×#95—472no—
373C2×#95—472no—
374C2×#95—472no—
375C2×#95C2×D4712yes—
376C2×#95C2×D4712yes—
377C47#1404011yescharacteristic, complemented, Sylow
378C25C22×D4711yescharacteristic
379C23×C4—22no—
380C23×C4—22no—
381C23×C4—22no—
382C23×C4—22no—
383C23×C4—22no—
384C23×C4—24no—
385C23×C4—24no—
386C23×C4—22no—
387C23×C4—22no—
388C23×C4—42no—
389C23×C4—42no—
390C23×C4—42no—
391C23×C4—42no—
392C23×C4—471no—
393C23×C4—472no—
394C23×C4—471no—
395C23×C4—471no—
396C23×C4—471no—
397C23×C4—472no—
398C23×C4C4×D4714yes—
399C23×C4C22⋊D4714yes—
400C23×C4C22×D4712yes—
401C23×C4C22×D4712yes—
402C23×C4C22×D4711yescharacteristic
403C23×C4C22×D4711yescharacteristic
404C2×C4⋊C4—478no—
405C2×C4⋊C4—1882no—
406C2×C4⋊C4—1882no—
407C2×C22⋊C4—474no—
408C2×C22⋊C4—474no—
409C2×C22⋊C4—474no—
410C2×C22⋊C4—942no—
411C2×C22⋊C4—942no—
412C2×C22⋊C4—942no—
413C2×C22⋊C4—942no—
414C2×C22⋊C4—942no—
415C2×C22⋊C4—942no—
416C2×C22⋊C4—942no—
417C2×C22⋊C4—942no—
418C2×C22⋊C4—942no—
419C2×C42—944no—
420C2×C42—942no—
421C2×C42—942no—
422C2×C42—1882no—
423#95—24no—
424#95—24no—
425#95—478no—
426#95—944no—
427#95—944no—
428#95—944no—
429#95—942no—
430#95—942no—
431#95—1882no—
432#95—1882no—
433#95—1882no—
434#95—1882no—
435#95—1882no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24C2×C4×D4712yes—
441C24#1062535012yes—
442C24#1062535212yes—
443C24#1062535212yes—
444C24Q8×D4712yes—
445C24#1062535412yes—
446C24C2×C22⋊D4712yes—
447C24C23×D4711yescharacteristic
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—28no—
452C22×C4—28no—
453C22×C4—28no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—28no—
471C22×C4—48no—
472C22×C4—44no—
473C22×C4—48no—
474C22×C4—48no—
475C22×C4—48no—
476C22×C4—48no—
477C22×C4—44no—
478C22×C4—44no—
479C22×C4—44no—
480C22×C4—48no—
481C22×C4—44no—
482C22×C4—472no—
483C22×C4—474no—
484C22×C4—472no—
485C22×C4—472no—
486C22×C4—472no—
487C22×C4—941no—
488C22×C4—941no—
489C22×C4—941no—
490C22×C4—941no—
491C22×C4—942no—
492C22×C4—942no—
493C22×C4—942no—
494C22×C4—942no—
495C22×C4—942no—
496C22×C4—942no—
497C22×C4—942no—
498C22×C4—941no—
499C22×C4—941no—
500C22×C4—942no—
501C22×C4—941no—
502C22×C4—941no—
503C22×C4—942no—
504C22×C4—942no—
505C22×C4—942no—
506C22×C4—942no—
507C22×C4—942no—
508C22×C4—942no—
509C22×C4—942no—
510C22×C4—942no—
511C22×C4—942no—
512C22×C4—942no—
513C22×C4—942no—
514C22×C4—942no—
515C22×C4—942no—
516C22×C4C2×C4×D4714yes—
517C22×C4#1062535014yes—
518C22×C4#1062535014yes—
519C22×C4C2×C22⋊D4712yes—
520C22×C4C2×C22⋊D4712yes—
521C4⋊C4—1888no—
522C22⋊C4—948no—
523C22⋊C4—948no—
524C22⋊C4—948no—
525C22⋊C4—1884no—
526C42—1884no—
527C42—1884no—
528C23—24no—
529C23—24no—
530C23—24no—
531C23—24no—
532C23—24no—
533C23—24no—
534C23—24no—
535C23—24no—
536C23—24no—
537C23—24no—
538C23—22no—
539C23—22no—
540C23—24no—
541C23—22no—
542C23—22no—
543C23—24no—
544C23#1309398214yes—
545C23C4×C22⋊D4714yes—
546C23#1309398914yes—
547C23#1309400014yes—
548C23#1309400514yes—
549C23#1309401414yes—
550C23#1309401914yes—
551C23C22×C4×D4711yescharacteristic
552C23C22×C22⋊D4711yescharacteristic
553C23C2×Q8×D4711yescharacteristic
554C23C2×#1062535211yescharacteristic
555C23C2×#1062535211yescharacteristic
556C23C2×#1062535012yes—
557C23C2×#1062535012yes—
558C23C2×#1062535011yescharacteristic
559C23C2×#1062535411yescharacteristic
560C23#1309406912yes—
561C23#1309406912yes—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—24no—
574C2×C4—22no—
575C2×C4—416no—
576C2×C4—416no—
577C2×C4—416no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—944no—
589C2×C4—944no—
590C2×C4—944no—
591C2×C4—942no—
592C2×C4—942no—
593C2×C4—944no—
594C2×C4—944no—
595C2×C4—944no—
596C2×C4—944no—
597C2×C4—942no—
598C2×C4—942no—
599C2×C4—1882no—
600C2×C4—1882no—
601C2×C4—1882no—
602C2×C4—1882no—
603C2×C4—1882no—
604C2×C4—1882no—
605C2×C4—1882no—
606C2×C4—1882no—
607C2×C4—1882no—
608C2×C4—1882no—
609C2×C4—1882no—
610C2×C4—1882no—
611C2×C4—1882no—
612C2×C4—1881no—
613C2×C4—1881no—
614C2×C4—1881no—
615C2×C4—1881no—
616C2×C4—1882no—
617C2×C4—1881no—
618C2×C4—1881no—
619C2×C4—1881no—
620C2×C4—1881no—
621C2×C4—1882no—
622C2×C4#1309400714yes—
623C22—24no—
624C22—28no—
625C22—28no—
626C22—24no—
627C22—24no—
628C22—28no—
629C22—24no—
630C22—24no—
631C22—24no—
632C22—28no—
633C22#1568900418yes—
634C22C2×#1309398211yescharacteristic
635C22C2×C4×C22⋊D4711yescharacteristic
636C22C2×#1309398911yescharacteristic
637C22C4×#1062535012yes—
638C22#1568959612yes—
639C22C2×#1309400011yescharacteristic
640C22C2×#1309400511yescharacteristic
641C22C2×#1309400711yescharacteristic
642C22#1568963411yescharacteristic
643C22C2×#1309401411yescharacteristic
644C22C2×#1309401911yescharacteristic
645C22#1568965712yes—
646C22#1568968211yescharacteristic
647C22#1568969011yescharacteristic
648C22#1568971112yes—
649C22#1568979912yes—
650C22#1568979912yes—
651C22#1568979912yes—
652C22#1568979912yes—
653C22#1568982112yes—
654C22#1568982112yes—
655C22#1568982812yes—
656C22#1568982812yes—
657C4—24no—
658C4—44no—
659C4—44no—
660C4—42no—
661C4—3762no—
662C4—1882no—
663C4—1884no—
664C4—1882no—
665C4—1882no—
666C4—1882no—
667C2—28no—
668C2C2×#1568900411yescharacteristic
669C2C4×#1309400711yescharacteristic
670C2#2024604611yescharacteristic
671C2#2024632412yes—
672C2#2024646812yes—
673C2#2024766211yescharacteristic
674C2#2024766611yescharacteristic
675C2#2024769911yescharacteristic
676C2#2024788912yes—
677C2#2024794812yes—
678C2#2024873511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC22×#95×C47C2
socle, cosocleC24×C47C24
prime radicalC25×C47C23
hypercenterC22×#95D47
hypocenterC47#14040
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×#95

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #20241654C2semidirect
4. #20241648C2semidirect
5. #20241619C2semidirect
6. #20241612C2semidirect
19. #15688996C4semidirect
46. C2×Dic47⋊C4C2×C4semidirect
73. C47⋊#95C2×C4semidirect
377. C47#14040semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#156889962
C2×C4×C22⋊Dic472
#202416542
#202416482
#202416192
#202416122
#202416112
C22×#95×C472
#1404047